Hear me out.
There's some obvious answers to that question, but I'm not looking for those answers.
Ever since the beta of GOG.com started, I've seen so many differentiating reasons why people support the service. I've seen reasons ranging from the "DRM is evil" stance to compatibility of these old games on modern systems.
So, what's your reason? Why do you support GOG with such enthusiasm?
To me, it's a combination of two major things: Low prices, and a distinct catalogue.
Being a hardcore PC gamer, I like to play as many games as I can, to have a proper opinion on the hobby. It's like music, you can't call yourself a music lover when you only listen to one artist/band. GOG can easily provide a way for me to diversify my tastes. Of the twenty-three GOG games I have, I only played a handful prior to GOG. Low prices make this incredibly easy as well, $5.99/$9.99 is more than enough to convince me to blind buy these games.
The extras are excellent, as well. Though, I wish each game came with more than just a manual. I think every game should have a wallpaper, at least one.
So, why do you?

I'm a young person (in my teens), and I want to play games that I couldn't play back in the 90s (because I was like, 3) and to support any kind of DRM-free movement. PC gaming is my hobby, and I want to try out different games (except Sensible Soccer... I hate that stuff).
And it's freaking cheap.

Price, lack of DRM, selection of "lost treasure" games... not necessarily in that order.

I can choose to buy my games elsewhere. Sold Out/Mastertronic still has some good old titles on sale. So does eBay. And of course, there's a local 2nd hand game community. However, I still choose to buy from GOG because of:
1) Excellent service
2) Lets you choose from a wide selection of genders
3) DRM-free
I would very much like to support GOG by giving them my money. Most people I know would call me crazy. I don't blame them for their pragmatism. After all, a game is a game, and as long as one can get it via whatever methods, it's fine to them. However to me, GOG has the courtesy of making the games almost 100% compatible with existing systems, taken the trouble of researching solutions to the problems that users face, and offer the games without charging extra for these services. That's quality service, something that's hard to find today

This.

1) Incredibly (almost impossibly) cheap prices
2) No DRM, no ET Phone Home, or anything else that restricts what I can do with it.
3) Just fantastic people who want nothing more than to make people happy.
Just a few of my reasons that I support GOG with the enthusiasm I do.
BJ

So, what's your reason? Why do you support GOG with such enthusiasm?
Basically, a cheap way in which I can enjoy games that I missed the first time around; and to get the chance to play games that I used to own again without having to worry about getting them to work (too much).

Its the price and people.

Low prices and no copy protection are the main points for me.
Although even minor stuff like the eye-catchy site design and easiness of buying add to it, i think.

I too enjoy GOG for the sexual variety it brings to my life. I originally came to GOG for the same reason I imagine most of us did -- because Duke Nuke'em made me question my sexuality.
Also, I like GOG for, in this order:
1. No DRM
2. Wrappers and seamless installation so I don't have to research games or spend any time setting them up to work on Vista.
3. No internet checks/spying/need for an internet connection to play the game anywhere, anytime.
4. Old favorites that are much too good to be forgotten. (Though I imagine at the rate they're acquiring games, that will change and we'll likely see more and more mediocre selections. Hope we won't get any stinkers though.) I like many of these old games much more than the new games I buy -- or don't.
The price is very nice too but not as much of a big deal to me. If I like it for 6 I"l like it for 10 and I might well like it for 20. Old games tend to be in that price range anyway, if you can find them (legally) at all.

-price
-additional bonus materials
-no DRM crap
-and hope that one day I will find here games which do I want to own (legally), so I could dispose of my remaining pirated CD's.

I like the community here.
I enjoy buying my games in a legal manner.
I also really love the fact that I can download the games I own here anytime i want without any hassle.
No DRM on games. Getting Gothic 2 Gold without the horrible DRM that wouldn't let you install or play the game = priceless.

I came from a scummvm link and thought it looked to be an interesting service.
After I added BASS, Lure and Teenagent to my online shelf I started looking more at the available titles here.
My ghost master disc is long since damaged beyond repair - but I loved that game... got it at release and kept an eye on the various forums when it came out.... Beig able to pick it up cheaply here to replace my broken copy ensuring that I didn't need to worry about a broken disc in future was a bonus.
I then found the forums to be very helpful and after reading the suggestions by a few people picked up The Guild - again no drm, quick and easy download/installation and it's kept on the online shelf here for re-installs.
I stay here and look with interest at announcements for the following:
1) Old games where my discs no longer work (properly) to replace via the online system here - Ghost Master being the initial example and if Evil Genius or Theme Hospital get added those would be purchased.
2) Old classics I missed for one reason or another that chatting with people on the forums have lead me to try - The Guild would be a good example here.
3) Pretty cheap games in general so I feel less bad about trying a game and if I don't like it a lot feeling like I wasted money - although I have a lot of purchases on Steam there is relatively little difference in cost between steam and retail... it's a bit silly really.
4) No DRM. I can buy a game on here and if I think my spouse would like it (we have similar tastes at times) I can put it on her PC to try without jumping through hoops.
5) The extras for the games in the catalogue. From a simple PDF manual to artistic concepts etc make a very nice touch. I hope that if they add games in the future that had pre-order bonuses (as an example) such as Evil Genius or Freedom Force they will be able to negotiate these as well.
6) Regionless... I greatly appreciate GoG taking the time to negotiate worldwide distribution rights. It is irritating as hell to see a game on an online service that sounds interesting only to find it is North America only (most common).
7) Online 'My Account' shelves. Being able to redownload and store purchased games on there is very nice - it saves reserving disc space here or burning discs. Hopefully the service makes them a profit and it continues. If it has to close at some point I hope GoG can give us enough heads up to download our collections for offline storage - and if ti does close there are no activation servers to worry about for future access of purchased games.

I like old games, I don't like DRM, I like the way they do business, and I got lured here by the Fallout games.
I'm desperate for them to expand their library to that I can get all the games from yesteryear without having to resort to piracy or abandonware.
I also want their "no-DRM" idea to spread to all distributers.

Judas, and all the IRC buffs force me to buy on here, yeah thats it! Damn bullies.
No, I buy it because I bloody love old games, I'm cheap as can be, and DRM is annoying. Also, IRC people are bullies. :(